I don't think there is a monster in the book; but there are some characters who do monstrous things.
Victor gives up his most important realtionships in an attempt to find a way to conquer death; in itself, his quest isn't all that different than our search to end disease, although the path he takes to achieve this may not have been the correct one. But the most monstrous thing he does is to create life, and then fail to love that life; in fact, he rejects it from the moment of its "birth." No matter how ugly/hideous his creation might have appeared, it was his obligation to love that which he had created. (This is always an odd part of the book; he had put together his creation from odd and oversized "pieces" of different individuals --- how could he be surprised at how it looked? Of course if you can believe that giving life to this collection of parts is possible, I guess you are expected to believe anything.) Add love to Victor's creation, and the story would be totally different.
And, of course, the creature does some monstrous things; he kills people and swears to and actually does wreck vengeance on his creator. Even though the intensity of his lonliness helps us understand his actions, they remain monstrous.
And the unspoken character in the story, society, is guilty of monstrous behavior toward the creature. If anyone had accepted him and tried to love him, if anyone had given him that one thing he most wanted, he who had been born pure and innocent might have stayed that way. If almost anyone had accepted the creature, all might have been well.
So who is the actual monster? I'll leave that up to you, but there is plenty of monstrous behaviour to go around.
This is a highly subjective question, with several answers supported by the text. Many people would argue that the creature is the actual monster. Indeed, he is hideous in form, unnaturally came into being, and cannot take any place in human society. He also kills mercilessly, taking the lives of innocent adults and children alike. Those who believe the creature to be the monster of the story would argue that nature (your DNA, if you will) is more important than nurture (the environment in which you grow). The creature has been a monster from the beginning, and he makes the choices to alienate himself from humans, and kill those whom he perceives as his torturers.
Others would argue that Victor is the monster. He has chosen to create the creature, and then chooses to abandon it when he sees it form. He is in the role of the "dead-beat dad" (if you'll forgive contemporary terminology). Even worse, he makes no attempt to stop the creature's actions. He lets Justine go to her execution, when he could have confessed and saved her. He also gives in to the creature's demands by making a female version, then destroys her, sealing his own fate. But in this action, he has also doomed Elizabeth as well. the creature later kills her for revenge. The sadness of Victor is that he has the power to bring these events to an end, but he's too much of a coward to act. Instead, he lets the creature wreak destruction on his family and friends. I tend to agree with this view.
Still others argue that it is Victor's mentality that is the true monster. Shelley seems to be suggesting this: "knowledge for knowledge's sake" isn't always a good thing, and indeed, can lead to disaster. At the time the novel was written, a new view of science was emerging. It was considered to be inherently good, with no regards to how information would be used, or what consequences would arise. This allows Victor to justify his creation, which some would say offends nature by its very existence.